Date of Award

2025

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Statistics (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Fan Dai

Committee Member 1

Qiuying Sha

Committee Member 2

Kui Zhang

Committee Member 3

Nathir A. Rawashdeh

Abstract

Factor analysis is a powerful tool for modeling latent structures in high-dimensional data, traditional approaches assume a single global structure, limiting their ability to capture heterogeneity. The Mixture of Factor Analyzers (MFA) extends classical factor analysis by modeling data as a mixture of Gaussian-distributed local subspaces, effectively uncovering cluster-specific latent structures. However, MFA relies on Gaussian mixtures, making it sensitive to outliers and ill-suited for heavy-tailed data. The Mixture of $t$-Factor Analyzers (M$t$FA) addresses these limitations by incorporating multivariate $t$-distributions, improving robustness. Despite their advantages, both MFA and M$t$FA face significant computational challenges in high-dimensional settings, particularly due to costly covariance matrix operations and slow convergence of the Expectation-Maximization (EM) algorithm. In this collection of work, we propose a hybrid approach that integrates a matrix-free algorithm within the EM framework to improve computational efficiency for both MFA and M$t$FA. Our methods preserve the full covariance structure while leveraging matrix-free strategies to optimize computations in high dimensions. This approach maintains the interpretability and flexibility of mixture-based factor models while making them more scalable. Empirical evaluations on synthetic and real-world data reveals that our method significantly improves speed, robustness, while preserving clustering accuracy compared to conventional MFA and M$t$FA models driven by standard EM algorithms. These findings highlight the effectiveness of matrix-free strategies in advancing mixture-based latent variable models for high-dimensional data analysis.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Available for download on Sunday, April 05, 2026

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